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Generalized Störmer-Cowell methods with efficient iterative solver for large-scale second-order stiff semilinear systems

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  • Chen, Hao
  • Yang, Yeru

Abstract

This paper studies the convergence and efficient implementation of generalized Störmer-Cowell methods (GSCMs) when they are applied to large-scale second-order stiff semilinear systems with the stiffness contained in the linear part. Theoretically, we prove that under some conditions the GSCMs are uniquely solvable and convergent of order p, where p is the consistence order of the methods. In practical computation, the discretized nonlinear algebraic equations can be implemented by a linear iterative scheme which is shown to be convergent. Meanwhile, a block triangular preconditioning strategy is proposed to solve the associated linear systems. Numerical tests are given to illustrate the effectiveness of the methods.

Suggested Citation

  • Chen, Hao & Yang, Yeru, 2021. "Generalized Störmer-Cowell methods with efficient iterative solver for large-scale second-order stiff semilinear systems," Applied Mathematics and Computation, Elsevier, vol. 400(C).
    • Handle: RePEc:eee:apmaco:v:400:y:2021:i:c:s0096300321001107
    DOI: 10.1016/j.amc.2021.126062
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    References listed on IDEAS

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    1. Li, Cui & Zhang, Chengjian, 2017. "The extended generalized Störmer–Cowell methods for second-order delay boundary value problems," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 87-95.
    2. Brugnano, L. & Frasca Caccia, G. & Iavernaro, F., 2015. "Energy conservation issues in the numerical solution of the semilinear wave equation," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 842-870.
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